Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Multi-core and many-core SPMD parallel algorithms for construction of basins of attraction

Treść / Zawartość
Warianty tytułu
Języki publikacji
Construction of basins of attraction, used for the analysis of nonlinear dynamical systems which present multistability, are computationaly very expensive. Because of the long runtime needed, in many cases, the construction of basins does not have any practical use. Numerical time integration is currently the bottleneck of algorithms used for the construction of such basins. The integrations related to each set of initial conditions are independent of each other. The assignment of each integration to a separate thread seems very attractive, and parallel algorithms which use this approach to construct the basins are presented here. Two versions are considered, one for multi-core and another for many-core architectures, both based on a SPMD approach. The algorithm is tested on three systems, the classic nonlinear Duffing system, a non-ideal system exhibiting the Sommerfeld effect and an immunodynamic system. The results for all examples demonstrate the versatility of the proposed parallel algorithm, showing that the multi-core parallel algorithm using MPI has nearly an ideal speedup and efficiency.
Opis fizyczny
Bibliogr. 27 poz., rys.
  • São Paulo State University – UNESP, Faculty of Engineering, Bauru, Brazil
  • São Paulo State University – UNESP, Faculty of Engineering, Bauru, Brazil
  • São Paulo State University – UNESP, Faculty of Engineering, Bauru, Brazil
  • 1. Agrawal O.P., Danhof K.J., Kumar R., 1992, A superelement model based parallel algorithm for vehicle dynamics, Computers and Structures, 51, 411423, DOI: 10.1016/0045-7949(94)90326-3
  • 2. Aktulga H.M., Fogarty J.C., Pandit S.A., Grama A.Y., 2012, Parallel reactive molecular dynamics: Numerical methods and algorithmic techniques, Parallel Computing, 38, 245259, DOI: 10.1016/j.parco.2011.08.005
  • 3. Balthazar J.M., Tusset A.M., Brasil R.M.L.R.F., Felix J.L.P., Rocha R.T., Janzen F.C., Nabarrete A., Oliveira C., 2018, An overview on the appearance of the Sommerfeld effect and saturation phenomenon in non-ideal vibrating systems (NIS) in macro and MEMS scales, Nonlinear Dynamics, 122, DOI: 10.1007/s11071-018-4126-0
  • 4. Belytschko T., Yen H.J., Mullen R., 1979, Mixed methods for time integration, Computer Methods in Applied Mechanics and Engineering, 1718, 259275, DOI: 10.1016/0045-7825(79)90022-7
  • 5. Bendtsen C., 1996, Highly stable parallel Runge-Kutta methods, Applied Numerical Mathematics, 21, 18, DOI: 10.1016/0168-9274(96)00003-7
  • 6. Bhalerao K.D., Crithcley J., Anderson K., 2012, An efficient parallel dynamics algorithm for simulation of large articulated robotics system, Mechanism and Machine Theory, 53, 8698, DOI: 10.1016/j.mechmachtheory.2012.03.001
  • 7. Brodtkorb A.R., Hagen T.R., Satra M.L., 2013, Graphics processing unit GPU programming strategies and trends in GPU computing, Journal of Parallel and Distributed Computing, 73, 413, DOI: 10.1016/j.jpdc.2012.04.003
  • 8. Cong N.H., 1996, Explicit symmetric Runge-Kutta-Nystr¨om methods for parallel computers, Computers and Mathematics with Applications, 31, 111121, DOI: 10.1016/0898-1221(95)00198-0
  • 9. Goncalves P.J.P., Silveira M., Pontes B.R. Jr., Balthazar J.M., 2014, Model analogy, numerical and experimental analysis of a cantilever beam with a coupled unbalanced non-ideal motor, Journal of Sound and Vibration, 333, 51155129, DOI: 10.1016/j.jsv.2014.05.039
  • 10. Goncalves P.J.P., Silveira M., Petrocino E.A., Balthazar J.M., 2015, Double resonance capture of a two-degree-of-freedom oscillator coupled to a non-ideal motor, Meccanica, DOI: 10.1007/s11012-015-0349-z
  • 11. Koziara T., Bićanić N., 2011, A distributed memory parallel multibody contact dynamics code, International Journal for Numerical Methods in Engineering, 87, 437456, DOI: 10.1002/nme.3158
  • 12. Lang J., Li M.Y., 2012, Stable and transient periodic oscillations in a mathematical model for CTL response to HTLV-I infection, Journal of Mathematical Biology, 65, 181199, DOI: 10.1007/s00285-011-0455-z
  • 13. Lenci S., Rega G., Ruzziconi L., 2013, The dynamical integrity concept for interpreting/prediction experimental behaviour: from macro- to nano-mechanics, Philosophical Transactions of the Royal Society A, 371, DOI: 10.1098/rsta.2012.0423
  • 14. McDonald S.W., Grebogi C., Ott E., Yorke J.A., 1985, Fractal basin boundaries, Physica D, 17, 125153, DOI: 10.1016/0167-2789(85)90001-6
  • 15. Michaels P., Zubik-Kowal B., 2012, Parallel computations and numerical simulations for nonlinear systems of Volterra integro-differential equations, Communications in Nonlinear Science and Numerical Simulation, 17, 30223030, DOI: 10.1016/j.cnsns.2011.11.006
  • 16. Modak S., Sotelino E.D., 2002, An object-oriented programming framework for the parallel dynamic analysis of structures, Computers and Structures, 80, 7784, DOI: 10.1016/S0045- 7949(01)00154-7
  • 17. Murty R., Okunbor D., 1999, Efficient parallel algorithms for molecular dynamics simulations, Parallel Computing, 25, 217230, DOI: 10.1016/S0167-8191(98)00114-8
  • 18. Nayfeh A.H., Balachandran B., 1995, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods, Wiley
  • 19. Pacheco P., 2011, An Introduction to Parallel Programming, Morgan Kaufmann
  • 20. Parker T.S., Chua L.O., 1992, Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag
  • 21. Ramachandramurthi S., Hallam T.G., Nichols J.A., 1997, Parallel simulation of individualbased, physiologically structured population models, Mathematical and Computer Modelling, 25, 5570, DOI: 10.1016/S0895-7177(97)00094-0
  • 22. Rao A.R.M., 2002, A parallel mixed time integration algorithm for nonlinear dynamic analysis, Advances in Engineering Software, 33, 261271, DOI: 10.1016/S0965-9978(02)00021-2
  • 23. Rega G., Lenci S., 2005, Identifying, evaluating, and controlling dynamical integrity measures in non-linear mechanical oscillators, Numerical Analysis, 63, 902914, DOI: 10.1016/
  • 24. Soliman M.S., Thompson J.M.T., 1989, Integrity measures quantifying the erosion of smooth and fractal basins of attraction, Journal of Sound and Vibration, 135, 453475, DOI: 10.1016/0022- 460X(89)90699-8
  • 25. Sommeijer B.P., 1993, Explicit, high-order Runge-Kutta-Nystrom methods for parallel computers, Applied Numerical Mathematics, 13, 221240, DOI: 10.1016/0168-9274(93)90145-H
  • 26. Thompson J.M.T., Stewart H.B., 2002, Nonlinear Dynamics and Chaos, John Wiley & Sons, 2nd edition
  • 27. Trobec R., Jerebic I., Janezic D., 1993, Parallel algorithm for molecular dynamics integration, Parallel Computing, 19, 10291039, DOI: 10.1016/0167-8191(93)90095-3
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.